Decorrelation-Based Feature Discovery: Parkinsons-Whole

1 Effect of UPSTM-Based Decorrelation on Feature Discovery

1.0.1 Loading the libraries

library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)

op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)

1.1 Material and Methods

Data from the speech features

1.2 The Data

pd_speech_features <- as.data.frame(read_excel("~/GitHub/FCA/Data/pd_speech_features.xlsx",sheet = "pd_speech_features", range = "A2:ACB758"))

1.2.1 The Average of the Three Repetitions

Each subject had three repeated observations. Here I’ll use the average of the three experiments per subject.

rep1Parkison <- subset(pd_speech_features,RID==1)
rownames(rep1Parkison) <- rep1Parkison$id
rep1Parkison$id <- NULL
rep1Parkison$RID <- NULL
rep1Parkison[,1:ncol(rep1Parkison)] <- sapply(rep1Parkison,as.numeric)

rep2Parkison <- subset(pd_speech_features,RID==2)
rownames(rep2Parkison) <- rep2Parkison$id
rep2Parkison$id <- NULL
rep2Parkison$RID <- NULL
rep2Parkison[,1:ncol(rep2Parkison)] <- sapply(rep2Parkison,as.numeric)

rep3Parkison <- subset(pd_speech_features,RID==3)
rownames(rep3Parkison) <- rep3Parkison$id
rep3Parkison$id <- NULL
rep3Parkison$RID <- NULL
rep3Parkison[,1:ncol(rep3Parkison)] <- sapply(rep3Parkison,as.numeric)

whof <- !(colnames(rep1Parkison) %in% c("gender","class"));
avgParkison <- rep1Parkison;
avgParkison[,whof] <- (rep1Parkison[,whof] + rep2Parkison[,whof] + rep3Parkison[,whof])/3


signedlog <- function(x) { return (sign(x)*log(abs(1.0e12*x)+1.0))}
whof <- !(colnames(avgParkison) %in% c("gender","class"));
avgParkison[,whof] <- signedlog(avgParkison[,whof])

1.2.1.1 Standarize the names for the reporting

studyName <- "Parkinsons"
dataframe <- avgParkison
outcome <- "class"

TopVariables <- 10

thro <- 0.80
cexheat = 0.15

1.3 Generaring the report

1.3.1 Libraries

Some libraries

library(psych)
library(whitening)
library("vioplot")
library("rpart")

1.3.2 Data specs

pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))

rows	col
252	753

pander::pander(table(dataframe[,outcome]))

0	1
64	188

varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]

largeSet <- length(varlist) > 1500 

1.3.3 Scaling the data

Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns

  ### Some global cleaning
  sdiszero <- apply(dataframe,2,sd) > 1.0e-16
  dataframe <- dataframe[,sdiszero]

  varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
  tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
  dataframe <- dataframe[,tokeep]

  varlist <- colnames(dataframe)
  varlist <- varlist[varlist != outcome]
  
  iscontinous <- sapply(apply(dataframe,2,unique),length) >= 5 ## Only variables with enough samples



dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData

1.4 The heatmap of the data

numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000


if (!largeSet)
{

  hm <- heatMaps(data=dataframeScaled[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 xlab="Feature",
                 ylab="Sample",
                 srtCol=45,
                 srtRow=45,
                 cexCol=cexheat,
                 cexRow=cexheat
                 )
  par(op)
}

1.4.0.1 Correlation Matrix of the Data

The heat map of the data

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  #cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
  cormat <- cor(dataframe[,varlist],method="pearson")
  cormat[is.na(cormat)] <- 0
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Original Correlation",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.9999951

1.5 The decorrelation

DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#> 
#>  Included: 744 , Uni p: 0.01657441 , Uncorrelated Base: 192 , Outcome-Driven Size: 0 , Base Size: 192 
#> 
#> 
 1 <R=1.000,thr=0.900,N=  472>, Top: 45( 4 )=[ 2 : 45 Fa= 45 : 0.944 ]( 45 , 280 , 0 ),<|>Tot Used: 325 , Added: 280 , Zero Std: 0 , Max Cor: 1.000
#> 
 2 <R=1.000,thr=0.900,N=  472>, Top: 62( 6 )[ 1 : 62 Fa= 107 : 0.900 ]( 62 , 204 , 45 ),<|>Tot Used: 416 , Added: 204 , Zero Std: 0 , Max Cor: 1.000
#> 
 3 <R=1.000,thr=0.900,N=  472>, Top: 42( 6 )[ 1 : 42 Fa= 146 : 0.900 ]( 41 , 88 , 107 ),<|>Tot Used: 457 , Added: 88 , Zero Std: 0 , Max Cor: 0.997
#> 
 4 <R=0.997,thr=0.900,N=  472>, Top: 17( 3 )[ 1 : 17 Fa= 160 : 0.900 ]( 16 , 25 , 146 ),<|>Tot Used: 461 , Added: 25 , Zero Std: 0 , Max Cor: 0.979
#> 
 5 <R=0.979,thr=0.900,N=  472>, Top: 1( 1 )[ 1 : 1 Fa= 160 : 0.900 ]( 1 , 1 , 160 ),<|>Tot Used: 461 , Added: 1 , Zero Std: 0 , Max Cor: 0.900
#> 
 6 <R=0.900,thr=0.800,N=  233>, Top: 78( 7 )=[ 2 : 78 Fa= 193 : 0.843 ]( 75 , 116 , 160 ),<|>Tot Used: 502 , Added: 116 , Zero Std: 0 , Max Cor: 0.986
#> 
 7 <R=0.986,thr=0.900,N=   18>, Top: 9( 1 )[ 1 : 9 Fa= 200 : 0.900 ]( 9 , 9 , 193 ),<|>Tot Used: 502 , Added: 9 , Zero Std: 0 , Max Cor: 0.901
#> 
 8 <R=0.901,thr=0.900,N=   18>, Top: 1( 1 )[ 1 : 1 Fa= 200 : 0.900 ]( 1 , 1 , 200 ),<|>Tot Used: 502 , Added: 1 , Zero Std: 0 , Max Cor: 0.898
#> 
 9 <R=0.898,thr=0.800,N=   46>, Top: 20( 1 )[ 1 : 20 Fa= 204 : 0.800 ]( 19 , 23 , 200 ),<|>Tot Used: 510 , Added: 23 , Zero Std: 0 , Max Cor: 0.840
#> 
 10 <R=0.840,thr=0.800,N=   46>, Top: 3( 1 )[ 1 : 3 Fa= 205 : 0.800 ]( 3 , 3 , 204 ),<|>Tot Used: 510 , Added: 3 , Zero Std: 0 , Max Cor: 0.797
#> 
 11 <R=0.797,thr=0.800,N=   46>
#> 
 [ 11 ], 0.7970144 Decor Dimension: 510 Nused: 510 . Cor to Base: 224 , ABase: 11 , Outcome Base: 0 
#> 
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]

pander::pander(sum(apply(dataframe[,varlist],2,var)))

57178

pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))

56034

pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))

4.68

pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))

3.41

1.5.1 The decorrelation matrix

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  
  UPSTM <- attr(DEdataframe,"UPSTM")
  
  gplots::heatmap.2(1.0*(abs(UPSTM)>0),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Decorrelation matrix",
                    cexRow = cexheat,
                    cexCol = cexheat,
                   srtCol=45,
                   srtRow=45,
                    key.title=NA,
                    key.xlab="|Beta|>0",
                    xlab="Output Feature", ylab="Input Feature")
  
  par(op)
}

1.6 The heatmap of the decorrelated data

if (!largeSet)
{

  hm <- heatMaps(data=DEdataframe[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 cexRow = cexheat,
                 cexCol = cexheat,
                 srtCol=45,
                 srtRow=45,
                 xlab="Feature",
                 ylab="Sample")
  par(op)
}

1.7 The correlation matrix after decorrelation

if (!largeSet)
{

  cormat <- cor(DEdataframe[,varlistc],method="pearson")
  cormat[is.na(cormat)] <- 0
  
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Correlation after IDeA",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  
  par(op)
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.7973791

1.8 U-MAP Visualization of features

1.8.1 The UMAP based on LASSO on Raw Data

if (nrow(dataframe) < 1000)
{
  classes <- unique(dataframe[1:numsub,outcome])
  raincolors <- rainbow(length(classes))
  names(raincolors) <- classes
  datasetframe.umap = umap(scale(dataframe[1:numsub,varlist]),n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
  text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])
}

1.8.2 The decorralted UMAP

if (nrow(dataframe) < 1000)
{

  datasetframe.umap = umap(scale(DEdataframe[1:numsub,varlistc]),n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After IDeA",t='n')
  text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])
}

1.9 Univariate Analysis

1.9.1 Univariate

univarRAW <- uniRankVar(varlist,
               paste(outcome,"~1"),
               outcome,
               dataframe,
               rankingTest="AUC")

100 : std_MFCC_2nd_coef 200 : app_entropy_log_3_coef 300 : app_LT_TKEO_mean_7_coef 400 : tqwt_entropy_log_dec_15 500 : tqwt_medianValue_dec_7
600 : tqwt_stdValue_dec_35 700 : tqwt_skewnessValue_dec_27

univarDe <- uniRankVar(varlistc,
               paste(outcome,"~1"),
               outcome,
               DEdataframe,
               rankingTest="AUC",
               )

100 : std_MFCC_2nd_coef 200 : La_app_entropy_log_3_coef 300 : La_app_LT_TKEO_mean_7_coef 400 : La_tqwt_entropy_log_dec_15 500 : tqwt_medianValue_dec_7
600 : La_tqwt_stdValue_dec_35 700 : tqwt_skewnessValue_dec_27

1.9.2 Final Table

univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")

##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
std_delta_delta_log_energy	23.4	0.469	22.8	0.461	0.653	0.798
std_delta_log_energy	24.3	0.477	23.8	0.441	0.634	0.794
std_9th_delta_delta	23.6	0.242	23.4	0.171	0.746	0.787
std_8th_delta_delta	23.7	0.240	23.4	0.150	0.725	0.780
std_7th_delta_delta	23.7	0.261	23.5	0.188	0.931	0.776
tqwt_entropy_log_dec_12	-39.6	0.239	-39.4	0.240	0.887	0.770
std_6th_delta_delta	23.8	0.277	23.5	0.172	0.945	0.768
std_8th_delta	24.4	0.245	24.2	0.163	0.981	0.767
std_9th_delta	24.4	0.249	24.1	0.185	0.398	0.764
tqwt_entropy_shannon_dec_12	30.3	1.993	32.1	1.703	0.196	0.763

topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]


pander::pander(finalTable)

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
std_delta_log_energy	24.335	0.4770	23.810	0.441	6.34e-01	0.794
La_tqwt_energy_dec_33	0.411	0.5961	1.089	0.909	6.55e-01	0.755
La_std_2nd_delta	0.462	0.1321	0.329	0.144	7.54e-01	0.754
La_tqwt_entropy_log_dec_29	0.330	0.4378	0.514	0.275	1.30e-07	0.753
mean_MFCC_2nd_coef	21.360	18.1116	1.716	27.881	4.61e-07	0.753
La_tqwt_kurtosisValue_dec_33	3.501	0.2616	3.258	0.389	2.39e-01	0.746
std_10th_delta	24.349	0.2615	24.131	0.182	9.82e-01	0.746
La_tqwt_entropy_log_dec_31	-4.198	0.0772	-4.283	0.128	4.27e-01	0.745
tqwt_kurtosisValue_dec_18	28.598	0.2876	28.395	0.144	9.92e-01	0.734
La_apq11Shimmer	2.150	0.1606	2.031	0.133	4.19e-01	0.734

dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")


pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))

mean	total	fraction
2.74	457	0.613

theCharformulas <- attr(dc,"LatentCharFormulas")


finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])


orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]

Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores")

finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])

	DecorFormula	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC	RAWAUC	fscores
std_delta_delta_log_energy	NA	23.357	0.4694	22.794	0.461	6.53e-01	0.798	0.798	NA
std_delta_log_energy	NA	24.335	0.4770	23.810	0.441	6.34e-01	0.794	0.794	2
std_delta_log_energy1	NA	24.335	0.4770	23.810	0.441	6.34e-01	0.794	NA	NA
std_9th_delta_delta	NA	23.630	0.2424	23.388	0.171	7.46e-01	0.787	0.787	NA
std_8th_delta_delta	NA	23.660	0.2395	23.428	0.150	7.25e-01	0.780	0.780	NA
std_7th_delta_delta	NA	23.732	0.2611	23.479	0.188	9.31e-01	0.776	0.776	NA
tqwt_entropy_log_dec_12	NA	-39.634	0.2389	-39.390	0.240	8.87e-01	0.770	0.770	NA
std_6th_delta_delta	NA	23.800	0.2765	23.548	0.172	9.45e-01	0.768	0.768	NA
std_8th_delta	NA	24.406	0.2448	24.175	0.163	9.81e-01	0.767	0.767	NA
std_9th_delta	NA	24.365	0.2490	24.134	0.185	3.98e-01	0.764	0.764	NA
tqwt_entropy_shannon_dec_12	NA	30.301	1.9928	32.106	1.703	1.96e-01	0.763	0.763	NA
La_tqwt_energy_dec_33	- (0.923)tqwt_energy_dec_31 + tqwt_energy_dec_33	0.411	0.5961	1.089	0.909	6.55e-01	0.755	0.509	0
La_std_2nd_delta	- (0.907)std_MFCC_2nd_coef + std_2nd_delta	0.462	0.1321	0.329	0.144	7.54e-01	0.754	0.630	0
La_tqwt_entropy_log_dec_29	- (1.010)tqwt_entropy_log_dec_28 + tqwt_entropy_log_dec_29	0.330	0.4378	0.514	0.275	1.30e-07	0.753	0.565	-1
mean_MFCC_2nd_coef	NA	21.360	18.1116	1.716	27.881	4.61e-07	0.753	0.753	NA
La_tqwt_kurtosisValue_dec_33	- (0.887)tqwt_kurtosisValue_dec_32 + tqwt_kurtosisValue_dec_33	3.501	0.2616	3.258	0.389	2.39e-01	0.746	0.628	-1
std_10th_delta	NA	24.349	0.2615	24.131	0.182	9.82e-01	0.746	0.746	4
La_tqwt_entropy_log_dec_31	+ tqwt_entropy_log_dec_31 - (0.891)tqwt_entropy_log_dec_33	-4.198	0.0772	-4.283	0.128	4.27e-01	0.745	0.548	0
tqwt_kurtosisValue_dec_18	NA	28.598	0.2876	28.395	0.144	9.92e-01	0.734	0.734	3
La_apq11Shimmer	- (0.907)locShimmer + apq11Shimmer	2.150	0.1606	2.031	0.133	4.19e-01	0.734	0.713	-1

1.10 Comparing IDeA vs PCA vs EFA

1.10.1 PCA

featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE)   #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous]) 
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)

#pander::pander(pc$rotation)


PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])


  gplots::heatmap.2(abs(PCACor),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "PCA Correlation",
                    cexRow = 0.5,
                    cexCol = 0.5,
                     srtCol=45,
                     srtRow= -45,
                    key.title=NA,
                    key.xlab="Pearson Correlation",
                    xlab="Feature", ylab="Feature")

1.10.2 EFA

EFAdataframe <- dataframeScaled

if (length(iscontinous) < 2000)
{
  topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)/2)
  if (topred < 2) topred <- 2
  
  uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE)  # EFA analysis
  predEFA <- predict(uls,dataframeScaled[,iscontinous])
  EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
  colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous]) 


  
  EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
  
  
    gplots::heatmap.2(abs(EFACor),
                      trace = "none",
    #                  scale = "row",
                      mar = c(5,5),
                      col=rev(heat.colors(5)),
                      main = "EFA Correlation",
                      cexRow = 0.5,
                      cexCol = 0.5,
                       srtCol=45,
                       srtRow= -45,
                      key.title=NA,
                      key.xlab="Pearson Correlation",
                      xlab="Feature", ylab="Feature")
}

1.11 Effect on CAR modeling

par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(rawmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
  }

pander::pander(table(dataframe[,outcome],pr))

	0	1
0	39	25
1	3	185

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.889	0.843	0.925
3	se	0.984	0.954	0.997
4	sp	0.609	0.479	0.729
6	diag.or	96.200	27.662	334.550

par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe,control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(IDeAmodel,main="IDeA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(IDeAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
  }

pander::pander(table(DEdataframe[,outcome],pr))

	0	1
0	53	11
1	8	180

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.925	0.885	0.954
3	se	0.957	0.918	0.981
4	sp	0.828	0.713	0.911
6	diag.or	108.409	41.474	283.372

par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
  plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
  text(PCAmodel, use.n = TRUE,cex=0.75)
  ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}

pander::pander(table(PCAdataframe[,outcome],pr))

	0	1
0	40	24
1	14	174

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.849	0.799	0.891
3	se	0.926	0.878	0.959
4	sp	0.625	0.495	0.743
6	diag.or	20.714	9.850	43.561

par(op)

1.11.1 EFA

  EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
  EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
  pr <- predict(EFAmodel,EFAdataframe,type = "class")
  
  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(EFAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
  }

  pander::pander(table(EFAdataframe[,outcome],pr))

	0	1
0	36	28
1	4	184

  pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.873	0.825	0.911
3	se	0.979	0.946	0.994
4	sp	0.562	0.433	0.686
6	diag.or	59.143	19.552	178.898

  par(op)